Utilization of Partitions in Graph Structures

<p>The utilization of partitions is essential for proving the properties of different types of graphs. Gallai-Ramsey problems and conjectures which require the Regularity lemma require unique methods to improve the bounds on known results. In this work the upper bounds for Gallai-Ramsey using $k$ colors is lowered to at most $k(n-1) +3n$ for even cycles and (2^k+3-3)n \log n for odd cycles. Also, with the ideas of partitions in mind, the Regularity lemma was used to show that it is possible to create short paths with a fixed end point in hopes of pursuing the Enomoto and Ota conjecture.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (restricted to Georgia Southern)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Hall, Martin L

Contributors dc:contributor

• Andrew Sills
• Hua Wang

• ETD
• Regularity
• Gallai-Ramsey
• Ramsey
• Partitions
• Cycles
• Paths
• Discrete Mathematics and Combinatorics

Repository record dc:identifier

https://digitalcommons.georgiasouthern.edu/etd/1047

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2087